The concession of two early goals proved the difference, as United's second season in the Premier League began in defeat at Bramall Lane.
Raul Jimenez and Romain Saiss put the visitors two goals in front inside the opening six minutes at S2 and despite creating several openings after the break, the Blades couldn't find a way back into the game.
For the clash against Wolves, boss Wilder handed Ramsdale his second Blades debut, whilst fellow newcomers Burke, Ampadu and Foderingham were named amongst the substitutes where they were also joined by Berge and McGoldrick.
The new season got off to the worst possible start for the Blades, as Wolves took the lead inside three minutes. Podence broke down the United right, beat a retreating Lundstram before crossing into the box where JIMENEZ side footed into the roof of the net. And it got even worse three minutes later as Wolves added a second. Ramsdale tipped over a Jimenez effort at the expense of a corner, from which SAISS rose highest to head past the United stopper from Neto's delivery.
With the visitors in front, the game was very open. United looked to get numbers forward where possible, without a lot of joy, whilst Wolves were happy to try and catch the hosts on the break with Traore's pace and Jimenez's touch causing problems. As the half hour approached, Baldock, Lundstram and then Fleck kept the ball alive, only for referee Dean to adjudge that Sharp had fouled Patricio who failed to gather cleanly.
Gradually, the Blades were asserting themselves onto Wolves, forcing a couple of corners in quick succession, with McBurnie seeing a header saved by Patricio from the second. Egan and McBurnie were both carded for fouls on Jimenez, prior to the latter winning a free kick in a dangerous position on the left and Moutinho headed behind for another corner as the first period drew to a close.
The Blades were quickly out of the blocks following the restart, but Stevens fired over from a promising position after McBurnie got the better of Boly from Norwood's diagonal ball forward. On 51 minutes, United came even closer to getting back into the game. Lundstram beat the offside trap and squared to Fleck who struck a low effort against the far post, before Coady's diverted Baldock's shot wide on the rebound.
United continued to do all the attacking in the second half and a marauding run forward from Egan created another opening, but Lundstram was unable to connect with Sharp's ball across goal, with Patricio beaten. Still United pressed, but Wolves, mainly because of Coady, held out at the expense of another couple of corners.
Wolves first real attack in the second period would have seen a third goal, but for the brilliance of Ramsdale, who denied Saiss with the help of at the woodwork, before Jimenez prodded the rebound wide. It was end-to-end again, Lundstram freed an overlapping Baldock, but Sharp couldn't keep his effort on target, with substitute McGoldrick involved in the build-up too.
Chances continued to come and go for both teams, McGoldrick was denied at one end, before Traore powered forward and sent a rasping effort over Ramsdale's bar. Sharp rifled home in the second phase from Fleck's corner, but the whistle had already been blown for a foul by Egan on Boly.
As the game entered the last ten minutes, Wolves started to threaten more often on the break, with Traore in a more advanced role. He beat O'Connell and Egan before seeing a deflection take a shot wide for a corner, from which Jimenez headed wide at the near post.
Typically, United pressed and pressed until the very end, but the ball just wouldn't drop favourably in the visitors box, despite an ever increasing corner tally as five minutes added time were signalled. Berge's cross picked out McBurnie and his header was destined to nestle in the goal before Saiss headed off the line, which summed up the Blades misfortune in front of goal.
Blades: Ramsdale, Baldock, Stevens, Fleck, O'Connell, Basham (McGoldrick 70), Lundstram, McBurnie, Sharp, Egan, Norwood (Berge 76).
Unused: Burke, Jagielka, Foderingham, Ampadu, Osborn.
Wolves: Patricio, Saiss, Coady, Boly, Marçal, Dendoncker, Moutinho (Ferreira 86), Traore, Podence (Neves 76), Jimenez, Neto (Buur 69).
Unused: Ruddy, Silva, Jota, Vinagre.
As it happened...
Wolves to kick-off and we're underway.
First free-kick goes to Wolves as Adama Traore is tripped on halfway.
The visitors win an attacking throw deep inside United's half, but Traore's eventual cross is headed clear.
Goal for Wolves.
Swift counter attack down the left from Daniel Podence, there's a 3 on 2 in the middle in favour of the visitors and Raul Jimenez's finish is first class as he rifles the ball past Ramsdale.
United on the back foot as a deep cross is chested down by Jimenez and his firm drive is tipped over by Ramsdale.
United concede from the resulting corner from Neto as Romain Saiss jumps above the defence to plant a header beyond Ramsdale
A lot of work to do for United now. An early test of character for Chris Wilder's side. The game has calmed down a little after the two goal start as the Blades try and get a foothold.
Sharp floored by Traore and a free-kick opportunity for the hosts.
Fleck sails in the cross but it is too close to Patricio who makes a routine claim.
Some tasty challenges flying in as O'Connell puts in a strong tackle on Traore. He's not high though and wins the ball, something like that just might get the Blades going...
United under pressure again as Egan heads clear a Moutinho free-kick. The ball is returned and it is all hands to the pump as the Blades' backline holds firm to clear a second time.
Traore dances around the outside of Enda Stevens and delivers, Egan there again with a diving header clear. Wolves gaining confidence again...
Jimenez is up for the this one.
Sells a lovely dummy on the edge of the area to bring the ball onto his left peg but drills the shot wide of the far post.
Some good moments for United.
Firstly, McBurnie with a great flick to find Sharp back to goal, he can't quite find the yard he needs to shoot. The ball is worked wide though and Stevens delivers a great cross which gives the Wolves defence something to think about. The offside flag is raised but this is better from United.
United enjoying a little more territory but the end product is quite there as Fleck sails a cross into the gloves of Patricio.
First yellow of the game as Egan's challenge on Jimenez sees him into Mike Dean's book.
Patricio forced into a save as he tips Basham's cross over the bar.
The away swinging corner is clear at the second attempt.
A deflected Baldock cross earns United another corner.
Norwood's delivery is met firmly by the head of McBurnie. Patricio well placed to make a save but this is better from United.
McBurnie into the book now as he takes out Jimenez with his follow through after initially getting a touch on the ball.
McBurnie wins a free-kick and Norwood's delivery flicks off a Wolves jersey and it's a corner.
Not the best delivery and Wolves clear at the near post.
United have enjoyed more of the game in the last 10 minutes but still no real clear cut chance for the Blades as we head into the last few minutes of the half.
One added minute.
Blades 0 v 2 Wolves
Early goals from Jimenez and Saiss have Wolves in a good position at the break.
Teams are back out for the second half...
United to get the second half underway, Billy Sharp kicks-off...
Early chance at the start of the second half as McBurnie wins a flick and Stevens pounces on the loose ball. It is a tight angle and Stevens blazes over under pressure.
Lovely ball low in behind to find the run of Lundstram. He latches onto the pass, steadies himself before playing it low to Fleck. His low shot looks destined for the corner but it canons the post and Baldock's follow up is deflected wide.
United's resulting corner is cleared but Blades gaining some momentum at the start of the second half.
Chance for Wolves now as Moutinho's corner is headed down and just wide by Saiss.
Signs that United are opening Wolves up now.
Egan brings the ball out from the back with a great run, he plays a one-two with McBurnie before playing in Sharp who decides to square it to Lundstram but there was just too much pace on the cross and it flashes across the six-yard box.
Good run by Sharp wins United a corner.
Norwood's delivery goes deep and it drops at the feet of Traore. Not sure he knows much about it but it sticks and he clears.
Nice build up play by United as Norwood pings a lovely ball wide but the attack breaks down as O'Connell's centre is too close to Patricio.
United are much brighter in the second half. Much more purpose and tempo in the play, but Wolves are holding firm at this stage.
Sharp taking up some great positions. Twice he's been picked out inside the area but his low cross seeking McBurnie has been cut out on both occasions.
Change for Wolves as Neto is replaced by Oskar Burr.
What a save!
Wolves could have wrapped it up as confusion between Norwood and Lundstram sees Wolves break. Saiss is though but his effort is superbly tipped onto the post by Ramsdale and the follow up is put wide.
Change for United as McGoldrick replaces Basham.
Chance for United.
Great play by Lundstram who plays Baldock in at the byline but his cut-back is put over by Sharp from a tight angle.
Wolves have pushed Traore further forward and they hit United on the counter but the winger's effort flies over.
Wolves change as Podence is replaced by Ruben Neves.
United also make a sub as Norwood is off and Sander Berge is on.
United have the ball in the net but the whistle had long since been blown after a push by McGoldrick.
Another counter from Wolves as Traore takes on O'Connell and Egan but his effort is deflected wide for a corner.
Brilliant run from the winger.
Jimenez flashes a header just wide from the resulting corner.
Wolves sub as Moutinho is replaced by Vito Ferreira.
Berge down the right finds Baldock, his low cross is blocked behind for a corner.
Disappointing from Lundstram who's corner is cleared at the near post.
Another United corner, this time from Fleck is deep, but Egan heads wide.
Five minutes added as Traore sees another shot deflected wide.
Berge with the cross from the right, header from McBurnie but Wolves clear off the line.
Blades 0 - 2 Wolves
Much better second half from United who hit a post through Fleck, but Wolves did the damage early and goals from Jimenez and Saiss seal the points.